Confidence Interval for a Proportion (1 of 3)

where p is the proportion in the sample, z depends on the level of
confidence desired, and σp, the standard
error of a proportion, is equal to:

where π is
the proportion in the population and N is
the sample size. Since π is not known, p
is used to estimate it. Therefore the estimated value of σp is:

As an example, consider a researcher wishing to estimate the proportion
of X-ray machines that malfunction and produce excess radiation. A random
sample of 40 machines is taken and 12 of the machines malfunction. The
problem is to compute the 95% confidence interval on π,
the proportion that malfunction in the population.